The undulating tripod gait as a model of the locomotion of walking fish.

A large subset of fishes capable of terrestrial walking exhibit strikingly similar gaits despite spanning across the phylogenetic space and having substantial differences in morphology. This recurrent pattern suggests the existence of shared mechanical principles underlying locomotor convergence. To investigate these principles, we analyze a common strategy we term the "undulating tripod gait", a coordinated pattern of axial body undulation coupled with alternating anterior contact with the ground. In this work, we model the undulating tripod gait by approximating a fish's axial undulation as three rigid segments rotating with respect to each other and representing the anterior contact as a rigid beam that alternates the contact with the surface on the left and right sides of the body. Here, we focus on the grey bichir, Polypterus senegalus, as a specific exemplar of the undulating tripod gait. We perform high-speed kinematic analyses of terrestrial locomotion to identify baseline gait parameters, which we then validate as broadly representative by comparing them to those of other distantly related walking fishes. Using these parameters, we simulate the model to explore how variations in morphology and joint kinematics influence forward progression, revealing that peak locomotor performance emerges under conditions closely matching those observed in P. senegalus. Finally, we translate the model into a physical robot, demonstrating that the same simple coordination of axial undulation and anterior contact produces effective forward locomotion in the real world. By capturing core mechanical features shared across morphologically diverse species, this framework advances our understanding of terrestrial walking in fishes and offers a mechanistic lens through which to examine the evolutionary origins of locomotion in early vertebrates.